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This paper aims to investigate an efficient power allocation algorithm for multiuser orthogonal frequency division multiplexing (MU-OFDM) cognitive radio (CR) systems that uses the peak power constraint to protect the primary users. Under this constraint, the high-complexity optimal power allocation algorithm for OFDM-based CR systems is not suited to determine the power distribution because the algorithm must iteratively perform the standard water-filling (WF) to determine whether or not the power in each assigned subcarrier is greater than the peak power. Instead of using the WF algorithm, we use the conditions that the optimal power distribution should be satisfied to design a simple method for fulfilling the peak power constraint in each assigned subcarrier and then updating the water level. Simulation results indicate that using the proposed efficient method to update the water level achieves a system capacity close to that of the optimal power allocation algorithm.